How to extrude properly?
It looks like you forgot to enable your subsurf modifier by clicking the eye icon:



Right before then he enables the subsurf modifier, which causes the smooth subdivided interpolation of the mesh you are seeing.

Note that since the subsurf modifier is a modifier, you can enable it and disable it whenever you want without having to worry about doing it before or after various modeling operations. In other words, you have extruded it correctly, it just won't display the subdivided mesh until you enable the modifier.